The standard representation of an aspheric optical surface is a power series added to a base conic. This dissertation considers alternate ways of describing an aspheric surface, and the effect of such alternate descriptions on the design of optical systems. In rare cases one may represent an aspheric by an expression in closed form that allows the system to yield imagery that is in some sense perfect. A new family of such systems, having perfect axial imagery, is described. In most cases one must represent an aspheric by a series of basis functions added to a base conic. Nonpolynomial basis functions are discussed and used to design several different lenses. They are shown to give better image quality than the same number, or a larger number, of polynomial series terms. When used as optimization variables, the nonstandard basis functions are shown to converge to a solution in fewer iterations, in some cases, than when power series variables were used. The increase in convergence rate is at least paritially offset by the fact that the nonstandard functions take longer to evaluate than polynomials. Optical testing of aspheric surfaces having nonpolynomial descriptions is discussed to the extent necessary to show the feasibility, in principle, of testing and manufacturing some of the design examples presented in the dissertation. When the idea of designing aspheric surfaces with nonstandard functions as variables is accepted, one needs to know which of the many possible such variables to use in a given application. Some methods of searching for the most appropriate variables are described. A hypothesis is presented on which types of optical systems will benefit from nonstandard aspheric representations, and which will be adequately designed with polynomial representations.

An analysis of the performance of simple refractive null compensators was done. Two types of correctors were studied--the Dall compensator and the Offner compensator. A framework was built for determining whether these simple null tests are adequate for a wide range of aspheric surfaces. Variables involved in determining a surface to be null tested are f-number, conic constant, and focal length. Examples are given on how to determine the best null test for several aspheric surfaces. Also of concern in the design of a null compensator was simplicity. Two elements were the maximum used for both compensators and all compensator surfaces were spherical.

Phase shifting interferometry is one of the most promising methods for testing aspheres. However, one will encounter the following problems when it is applied to test an asphere: (1) very tight fringes produced by a strong asphere exceed the test system's resolution, (2) a test wavefront suffers from system aberrations of the interferometer that cause measurement errors, and (3) the wavefront immediately after reflection does not necessarily represent the shape of the test asphere. This thesis used a high density array sensor to detect the dense fringes. In order to solve the system aberration and the ray retrace problems, it is necessary to incorporate a ray trace code and phase shifting interferometry. This measurement principle was applied for an aspheric surface whose asphericity was 100 waves. A phase shifting Fizeau interferometer was incorporated with an optical design program. The attained accuracy was approximately one-tenth of a wave.

Thesis (Ph. D.)--Ohio State University, 2006. / Title from first page of PDF file. Includes bibliographical references (p. 167-175).

QC 351 A7 no. 69 / The history of modern wide -field, high-speed catadioptric lenses is reviewed. One system comprising only spherical curves and representative of the current art for low-light-level systems is evaluated and used as a baseline design in a weight-reduction study. Five aspheric designs are computed and evaluated. It is found that the use of aspherics will permit weight reduction only in certain instances, i.e., if one element of an all-spherical design can be eliminated or if a fundamentally different configuration that is possible only with aspherics is substituted for the all-spherical configuration. Of these possibilities, the elimination of an element is the best replacement for the baseline design. The case of a highly constrained, purely refractive triplet is studied in some detail. Four designs are computed -from the all-spherical case to the most complex polynomial aspheric. It is found that, if only conic aspherics are employed, significant improvement can be obtained and the problems involved are sensibly the same as those in all-spherical designs. When complex aspherics are applied, the problem becomes surprisingly difficult, and there is some indication that a computer can deal with it better than can a human lens designer.